Measuring how central nodes are in terms of connecting a network has recently received increasing attention in the literature. While a few dedicated centrality measures have been proposed, Skibski et al. [2016] showed that the Attachment Centrality is the only one that satisfies certain natural axioms desirable for connectivity. Unfortunately, the Attachment Centrality is defined only for unwei...

—Opportunistic networks exploit human mobility and consequent device-to-device contacts to opportunistically create data paths over time. Identifying influential nodes as relay is a crucial problem for efficient routing in opportunistic networks. The degree centrality method is very simple but of little relevance. Although closeness centrality and betweenness centrality can effectively identif...

Eigenvector-based centrality measures are among the most popular centrality measures in network science. The underlying idea is intuitive and the mathematical description is extremely simple in the framework of standard, mono-layer networks. Moreover, several efficient computational tools are available for their computation. Moving up in dimensionality, several efforts have been made in the pas...

Eigenvector centrality is a common measure of the importance of nodes in a network. Here we show that under common conditions the eigenvector centrality displays a localization transition that causes most of the weight of the centrality to concentrate on a small number of nodes in the network. In this regime the measure is no longer useful for distinguishing among the remaining nodes and its ef...

Recent developments in network theory have allowed for the study of the structure and function of the human brain in terms of a network of interconnected components. Among the many nodes that form a network, some play a crucial role and are said to be central within the network structure. Central nodes may be identified via centrality metrics, with degree, betweenness, and eigenvector centralit...

We study network centrality based on dynamic influencepropagation models in social networks. To illustrate our in-tegrated mathematical-algorithmic approach for understand-ing the fundamental interplay between dynamic influenceprocesses and static network structures, we focus on twobasic centrality measures: (a) Single Node Influence (SNI)centrality, which measures each ...

Centrality analysis determines the importance of vertices in a network based on their connectivity within the network structure. It is a widely used technique to analyse network-structured data. A particularly important task is the comparison of different centrality measures within one network. We present three methods for the exploration and comparison of centrality measures within a network: ...

In many real-life networks, such as urban structures, protein interactions and social networks, one of the key issues is to measure the centrality of nodes, i.e. to determine which nodes and edges are more central to the functioning of the entire network than others. In this paper we focus on betweenness centrality — a metric based on which the centrality of a node is related to the number of s...

Abstract To measure node importance, network scientists employ centrality scores that typically take a microscopic or macroscopic perspective, relying on features global structure. However, traditional measures such as degree centrality, betweenness PageRank neglect the community structure found in real-world networks. study importance based flows from mesoscopic we analytically derive communit...